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U1Gate

U1Gate(theta, label=None) GitHub(opens in a new tab)

Single-qubit rotation about the Z axis.

This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration).

Circuit symbol:

     ┌───────┐
q_0:U1(λ)
     └───────┘

Matrix Representation:

U1(λ)=(100eiλ)\begin{split}U1(\lambda) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\lambda} \end{pmatrix}\end{split}

Examples:

U1(λ=π)=ZU1(\lambda = \pi) = Z U1(λ=π/2)=SU1(\lambda = \pi/2) = S U1(λ=π/4)=TU1(\lambda = \pi/4) = T
See also

RZGate: This gate is equivalent to RZ up to a phase factor.

U1(λ)=eiλ/2RZ(λ)U1(\lambda) = e^{i{\lambda}/2} RZ(\lambda)

U3Gate: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses.

Reference for virtual Z gate implementation: 1612.00858(opens in a new tab)

Create new U1 gate.


Attributes

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

label

str

Return gate label

Return type

str

params

return instruction params.


Methods

add_decomposition

U1Gate.add_decomposition(decomposition)

Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble

U1Gate.assemble()

Assemble a QasmQobjInstruction

Return type

Instruction

broadcast_arguments

U1Gate.broadcast_arguments(qargs, cargs)

Validation and handling of the arguments and its relationship.

For example, cx([q[0],q[1]], q[2]) means cx(q[0], q[2]); cx(q[1], q[2]). This method yields the arguments in the right grouping. In the given example:

in: [[q[0],q[1]], q[2]],[]
outs: [q[0], q[2]], []
      [q[1], q[2]], []

The general broadcasting rules are:

  • If len(qargs) == 1:

    [q[0], q[1]] -> [q[0]],[q[1]]
  • If len(qargs) == 2:

    [[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]]
    [[q[0]], [r[0], r[1]]]       -> [q[0], r[0]], [q[0], r[1]]
    [[q[0], q[1]], [r[0]]]       -> [q[0], r[0]], [q[1], r[0]]
  • If len(qargs) >= 3:

    [q[0], q[1]], [r[0], r[1]],  ...] -> [q[0], r[0], ...], [q[1], r[1], ...]

Parameters

  • qargs (List) – List of quantum bit arguments.
  • cargs (List) – List of classical bit arguments.

Return type

Tuple[List, List]

Returns

A tuple with single arguments.

Raises

CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.

c_if

U1Gate.c_if(classical, val)

Add classical condition on register classical and value val.

control

U1Gate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a (mutli-)controlled-U1 gate.

Parameters

  • num_ctrl_qubits (int) – number of control qubits.
  • label (str or None) – An optional label for the gate [Default: None]
  • ctrl_state (int or str or None) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.

Returns

controlled version of this gate.

Return type

ControlledGate

copy

U1Gate.copy(name=None)

Copy of the instruction.

Parameters

name (str) – name to be given to the copied circuit, if None then the name stays the same.

Returns

a copy of the current instruction, with the name

updated if it was provided

Return type

qiskit.circuit.Instruction

inverse

U1Gate.inverse()

Return inverted U1 gate (U1(λ)=U1(λ)U1(\lambda){\dagger} = U1(-\lambda))

is_parameterized

U1Gate.is_parameterized()

Return True .IFF. instruction is parameterized else False

mirror

U1Gate.mirror()

For a composite instruction, reverse the order of sub-gates.

This is done by recursively mirroring all sub-instructions. It does not invert any gate.

Returns

a fresh gate with sub-gates reversed

Return type

qiskit.circuit.Instruction

power

U1Gate.power(exponent)

Creates a unitary gate as gate^exponent.

Parameters

exponent (float) – Gate^exponent

Returns

To which to_matrix is self.to_matrix^exponent.

Return type

qiskit.extensions.UnitaryGate

Raises

CircuitError – If Gate is not unitary

qasm

U1Gate.qasm()

Return a default OpenQASM string for the instruction.

Derived instructions may override this to print in a different format (e.g. measure q[0] -> c[0];).

repeat

U1Gate.repeat(n)

Creates an instruction with gate repeated n amount of times.

Parameters

n (int) – Number of times to repeat the instruction

Returns

Containing the definition.

Return type

qiskit.circuit.Instruction

Raises

CircuitError – If n < 1.

to_matrix

U1Gate.to_matrix()

Return a numpy.array for the U1 gate.

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